A052581 E.g.f. (1-x)/(1-x-x^4).

1, 0, 0, 0, 24, 120, 720, 5040, 80640, 1088640, 14515200, 199584000, 3353011200, 62270208000, 1220496076800, 24845812992000, 543992537088000, 12804747411456000, 320118685286400000, 8393511928209408000

Offset

0,5

Comments

Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)(1 - 2 S); see A291000. - Clark Kimberling, Aug 24 2017

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 525

Formula

E.g.f.: (-1+x)/(-1+x^4+x)

Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=0, (-n^4-35*n^2-50*n-24-10*n^3)*a(n) +(-n-4)*a(n+3) +a(n+4)=0}

Sum(-1/283*(9+12*_alpha^3+16*_alpha^2-73*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!

a(n)= n!*A017898(n). - R. J. Mathar, Nov 27 2011

Maple

spec := [S, {S=Sequence(Prod(Z, Z, Z, Z, Sequence(Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 27 2016 *)

Crossrefs

Sequence in context: A124657 A342856 A293050 * A052605 A195917 A334189

Adjacent sequences: A052578 A052579 A052580 * A052582 A052583 A052584

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved